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CHAPTER 8 : FORECASTING

What is forecasting?
• The use of historic data to determine the direction

of future trends. • Investors utilize forecasting to determine if events affecting a company, such as sales expectations, will increase or decrease the price of shares in that company.

• Forecasting also provides an important benchmark for firms which have a long-term perspective of operations.

What is forecasting?
• Forecasting is used by companies to determine how to allocate their budgets for an upcoming period of time. And typically based on demand for the goods and services it offers, compared to the cost of producing them.

Why is forecasting important?
Demand for products and services is usually uncertain. Forecasting can be used for:

What is forecasting all about?
Demand
We try to predict the future by looking back at the past
Jan Feb Mar Apr May Jun Jul Aug
Time
Predicted demand looking back six months
Actual demand (past sales)
Predicted demand
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Some general characteristics of forecasts
• Forecasts are rarely perfect • Forecasts are more accurate for groups or families of items • Forecasts are more accurate for shorter time periods • Every forecast should include an error estimate • Forecasts are no substitute for calculated demand.
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think carefully whether or not the past is strongly related to what you expect to see in the future
.: there is no such thing as a perfect forecast)
REMEMBER: Forecasting is based on the assumption that the past predicts the future! When forecasting. A forecast is only as good as the information included in the forecast (past data) 2.e. History is not a perfect predictor of the future (i.Key issues in forecasting
1.

Rely on data and analytical techniques.
.Types of forecasting methods
Qualitative methods Quantitative methods
Rely on subjective opinions from one or more experts.

Qualitative forecasting methods
Grass Roots: deriving future demand by asking the person closest to the customer. Panel Consensus: deriving future estimations from the synergy of a panel of experts in the area. Historical Analogy: identifying another similar market. new product ideas.
. Delphi Method: similar to the panel consensus but with concealed identities. Market Research: trying to identify customer habits.

Quantitative forecasting methods
Time Series: models that predict future demand based on past history trends
Causal Relationship: models that use statistical techniques to establish relationships between various items and demand
Simulation: models that can incorporate some randomness and non-linear effects
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Time Series: Moving average
• The moving average model uses the last t periods in order to predict demand in period t+1. • There are two types of moving average models: simple moving average and weighted moving average • The moving average model assumption is that the most accurate prediction of future demand is a simple (linear) combination of past demand.
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A is the actual sales figure from each period.Time series: simple moving average
In the simple moving average models the forecast value is
At + At-1 + … + At-n Ft+1 = n
t is the current period.
Ft+1 is the forecast for next period
n is the forecasting horizon (how far back we look).
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is the importance (weight) we give to each period
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Ft+1 is the forecast for next period
n
A w
is the forecasting horizon (how far back we look).
is the actual sales figure from each period.Time series: weighted moving average
We may want to give more importance to some of the data
Ft+1 =
t
wt At + wt-1 At-1 + … + wt-n At-n
wt + wt-1 + … + wt-n = 1
is the current period.

Why do we need the WMA models?
Because of the ability to give more importance to what happened recently. attributing equal weights to all past data we miss the downward trend
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Demand for Mercedes E-class
Actual demand (past sales) Prediction when using 6-month SMA Prediction when using 6-months WMA
Jan Feb Mar Apr May Jun Jul Aug
Time
For a 6-month SMA. without losing the impact of the past.

the more we pick up the declining trend in our forecast.247
The higher the importance we give to recent data .277
WMA 40% / 60% 1.267
WMA 30% / 70% 1.257
WMA 20% / 80% 1.
.What if we use a weighted moving average?
Make the weights for the last three months more than the first three months
6-month SMA July Forecast 1.

Depending on known seasonality (weights of past data can also be zero).
WMA is better than SMA because of the ability to vary the weights!
.How do we choose weights?
1. Depending on the importance that we feel past data has
2.

Time Series: Exponential Smoothing (ES)
Main idea: The prediction of the future depends mostly on the most recent observation.
Smoothing constant alpha α
Denotes the importance of the past error
. and on the error for the latest forecast.

value to be kept same requires that distribution the past k of forecast data points error when be kept α = 2/(k+1).Comparison of Exponential Smoothing with moving average
only needs Exponential same smoothing distribution the most takes into account all past data only takes into account k past data points.
moving average
of forecast recent error when forecast α = 2/(k+1). time series. not trending.
. therefore lagging behind the trend if one exists.
Exponential smoothing and moving average are similar as both assume a stationary.

If α is high: there is a lot of reaction to differences.Exponential smoothing: the method
Assume that we are currently in period t. We calculated the forecast for the last period (Ft-1) and we know the actual demand last period (At-1) …
Ft  Ft1   ( At1  Ft1 )
The smoothing constant α expresses how much our forecast will react to observed differences… If α is low: there is little reaction to differences.
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we are trying to explore which independent variables affect the dependent variable
.Linear regression in forecasting
Linear regression is based on
1. Fitting a straight line to data
2.
dependent variable = a + b  (independent variable)
By using linear regression. Explaining the change in one variable through changes in other variables.

Example: do people drink more when it’s cold?
Alcohol Sales Which line best fits the data?
Average Monthly Temperature
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The best line is the one that minimizes the error
The predicted line is
Y  a  bX
So.Yi
Where: ε is the error y is the observed value Y is the predicted value
. the error is
εi  yi .

Least Squares Method of Linear Regression
The goal of LSM is to minimize the sum of squared errors
What does that mean?
Min
 i2 
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the arrows hit the Bulls eye (so much for averages!)
High MFE & MAD:
The forecasts are inaccurate & biased
.MFE & MAD: A Dartboard Analogy
Low MFE & MAD: The forecast errors are small & unbiased
Low MFE but high MAD:
On average.

Key Point
Forecast must be measured for accuracy!
The most common means of doing so is. by measuring either the mean absolute deviation or the standard deviation of the forecast error
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investigate!
. It is used to decide when to re-evaluate using a model.
RSFE  (At  Ft )
i1
n
RSFE TS  MAD
Positive tracking signal: most of the time actual values are above our forecasted values Negative tracking signal: most of the time actual values are below our forecasted values
If TS > 4 or < -4.Measuring Accuracy: Tracking signal
The tracking signal is a measure of how often our estimations have been above or below the actual value.

0
33
.6.0
We observe that FIT performs a lot better than ES Conclusion: Probably there is trend in the data which Exponential smoothing cannot capture
.2.Bottled water at Kroger: compare MAD and TS
MAD Exponential Smoothing Forecast Including Trend TS
70
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Which Forecasting Method Should You Use
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Which Forecasting Method Should You Use
• Gather the historical data of what you want to forecast • Divide data into initiation set and evaluation set • Use the first set to develop the models • Use the second set to evaluate • Compare the MADs and MFEs of each model to determine the forecast accuracy
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